Star Formation with Adaptive Mesh Refinement Radiation Hydrodynamics

I provide a pedagogic review of adaptive mesh refinement (AMR) radiation hydrodynamics (RHD) methods and codes used in simulations of star formation, at a level suitable for researchers who are not computational experts. I begin with a brief overview of the types of RHD processes that are most important to star formation, and then I formally introduce the equations of RHD and the approximations one uses to render them computationally tractable. I discuss strategies for solving these approximate equations on adaptive grids, with particular emphasis on identifying the main advantages and disadvantages of various approximations and numerical approaches. Finally, I conclude by discussing areas ripe for improvement.Comment: 8 pages, to appear in the Proceedings of IAU Symposium 270: Computational Star Formatio

A Work Program for Equity Planners

During the mid-twentieth century period of Title I urban renewal, planners operated in a field that featured big plans and bold projects. Urban renewal was an approach in which well-meaning people set out to clean up our messy cities and many of the people who lived in them through large-scale projects. This approach was supported by law and a general consensus that the demolition of substandard housing was a good thing. But, like the rest of us, poor people need housing too, and bitter struggles over urban renewal displacements forced politicians to end the program in 1974. Today, few planners are involved in planning for giant projects. Unlike architects who see the city as a world of built forms, or developers who rarely see the city at all but see only packages of potential profit, most planners see a more comprehensive picture. The way planners see their cities is important, because of their power to influence land use decisions and because their code of ethics directs them to expand choice and opportunity for all persons, recognizing a special responsibility to plan for the needs of disadvantaged populations (AICP, 2010)

From Planning Practice to Academia

By tracing his journey from city planning director to director of a technical assistance center within a large university, Norman Krumholz explores the importance of bridging the gap between the study and practice of planning. In so doing, he states that each of these very different worlds has a great deal to gain from the other

The Power Spectrum of Turbulence in NGC 1333: Outflows or Large-Scale Driving?

Is the turbulence in cluster-forming regions internally driven by stellar outflows or the consequence of a large-scale turbulent cascade? We address this question by studying the turbulent energy spectrum in NGC 1333. Using synthetic 13CO maps computed with a snapshot of a supersonic turbulence simulation, we show that the VCS method of Lazarian and Pogosyan provides an accurate estimate of the turbulent energy spectrum. We then apply this method to the 13CO map of NGC 1333 from the COMPLETE database. We find the turbulent energy spectrum is a power law, E(k) k^-beta, in the range of scales 0.06 pc < ell < 1.5 pc, with slope beta=1.85\pm 0.04. The estimated energy injection scale of stellar outflows in NGC 1333 is ell_inj 0.3 pc, well resolved by the observations. There is no evidence of the flattening of the energy spectrum above the scale ell_inj predicted by outflow-driven simulations and analytical models. The power spectrum of integrated intensity is also a nearly perfect power law in the range of scales 0.16 pc < ell < 7.9 pc, with no feature above ell_inj. We conclude that the observed turbulence in NGC 1333 does not appear to be driven primarily by stellar outflows.Comment: Submitted to APJ Letters on September 22, 2009 - Accepted on November 18, 200

Global star formation revisited

A general treatment of disk star formation is developed from a dissipative multi-phase model, with the dominant dissipation due to cloud collisions. The Schmidt-Kennicutt law emerges naturally for star-forming disks and starbursts. We predict that there should be an inverse correlation between Tully-Fisher law and Schmidt-Kennicutt law residuals. The model is extended to include a multi-phase treatment of supernova feedback that leads to a turbulent pressure-regulated generalization of the star formation law and is applicable to gas-rich starbursts. Enhanced pressure, as expected in merger-induced star formation, enhances star formation efficiency. An upper limit is derived for the disk star formation rate in starbursts that depends on the ratio of global ISM to cloud pressures. We extend these considerations to the case where the interstellar gas pressure in the inner galaxy is dominated by outflows from a central AGN. During massive spheroid formation, AGN-driven winds trigger star formation, resulting in enhanced supernova feedback and outflows. The outflows are comparable to the AGN-boosted star formation rate and saturate in the super-Eddington limit. Downsizing of both SMBH and spheroids is a consequence of AGN-driven positive feedback. Bondi accretion feeds the central black hole with a specific accretion rate that is proportional to the black hole mass. AGN-enhanced star formation is mediated by turbulent pressure and relates spheroid star formation rate to black hole accretion rate. The relation between black hole mass and spheroid velocity dispersion has a coefficient (Salpeter time to gas consumption time ratio) that provides an arrow of time. Highly efficient, AGN-boosted star formation can occur at high redshift.Comment: Astrophysical Journal, in press (references added

The Structure of the Interstellar Medium of Star Forming Galaxies

We present numerical methods for including stellar feedback in galaxy-scale simulations. We include heating by SNe (I & II), gas recycling and shock-heating from O-star & AGB winds, HII photoionization, and radiation pressure from stellar photons. The energetics and time-dependence are taken directly from stellar evolution models. We implement these in simulations with pc-scale resolution, modeling galaxies from SMC-like dwarfs and MW analogues to massive z~2 starburst disks. Absent feedback, gas cools and collapses without limit. With feedback, the ISM reaches a multi-phase steady state in which GMCs continuously form, disperse, and re-form. Our primary results include: (1) Star forming galaxies generically self-regulate at Toomre Q~1. Most of the volume is in diffuse hot gas with most of the mass in dense GMC complexes. The phase structure and gas mass at high densities are much more sensitive probes of stellar feedback physics than integrated quantities (Toomre Q or gas velocity dispersion). (2) Different feedback mechanisms act on different scales: radiation & HII pressure are critical to prevent runaway collapse of dense gas in GMCs. SNe and stellar winds dominate the dynamics of volume-filling hot gas; however this primarily vents out of the disk. (3) The galaxy-averaged SFR is determined by feedback. For given feedback efficiency, restricting star formation to molecular gas or modifying the cooling function has little effect; but changing feedback mechanisms directly translates to shifts off the Kennicutt-Schmidt relation. (4) Self-gravity leads to marginally-bound GMCs with an ~M^-2 mass function with a cutoff at the Jeans mass; they live a few dynamical times before being disrupted by stellar feedback and turn ~1-10% of their mass into stars (increasing from dwarfs through starburst galaxies). Low-mass GMCs are preferentially unbound.Comment: 34 pages, 24 figures, accepted to MNRAS (matches accepted version). Movies of the simulations are available at https://www.cfa.harvard.edu/~phopkins/Site/Movies_sbw.htm

Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence

We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method, and using little to no explicit artificial viscosity. Codes which fall short in one or more of these areas are still useful, but they must compensate higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices in picking optimal applications for their specific astrophysical problems.Comment: 17 pages, 5 color figures, revised version to appear in ApJ, 735, July 201